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The Structure of Elementary Strategies for Gene Assembly in Ciliates

Rogojin V., Petre I.

Fundamenta Informaticae

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2015

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Vol. 138, nr 1/2

145--158

EN

We consider in this paper the assembly of micronuclear genes in stichotrichous ciliates to their macronuclear form. We represent the micronuclear genes and all their intermediate forms from micro- to macro- as signed permutations, where integer i stands for the i-th MDS of the macronuclear gene and i stands for the inverted form of that MDS; the macronuclear assembled gene is represented as the sorted permutation 1 2 : : : n, while its micronuclear form is an arbitrary signed permutation. We focus on the elementary gene assembly model consisting of two operations on signed permutations: eh (elementary hairpin inverting) and ed (elementary double recombination); gene assembly is modeled in this framework as a permutation sorting process. The general problem we investigate is to give a characterization of all signed permutations that can be sorted by the elementary operations. We make progress towards a full solution for this problem by relating sequences of eh and ed operations applicable to a given permutation to paths in the dependency graph associated to that permutation.

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Directed Overlap-inclusion Graphs as Representations of Ciliate Genes

Azimi S., Harju T., Langille M., Petre I., Rogojin V.

Fundamenta Informaticae

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2011

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Vol. 110, nr 1-4

29-44

EN

The simple intramolecular model for gene assembly in ciliates consists of three molecular operations based on local DNA manipulations. It was shown to predict correctly the assembly of all currently known ciliate gene patterns. Mathematical models in terms of signed permutations and signed strings proved limited in capturing some of the combinatorial details of the simple gene assembly process. A different formalization in terms of overlap-inclusion graphs, recently introduced by Brijder and Hoogeboom, proved well-suited to describe two of the three operations of the model and their combinatorial properties. We introduce in this paper an extension of the framework of Brijder and Hoogeboom in terms of directed overlap-inclusion graphs where more of the linear structure of the ciliate genes is described. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs.

3

A Better-developed soil profile during biblical times in the western Galilee. 15N evidence in 14C - dated groundwater

Rogojin V., Kronfeld J., Carmi I., Talma A. S.

Geochronometria

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2002

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Vol. 21

79-84

EN

Despite almost a hundred years of reforestation efforts, the recharge area of the Judea Group aquifer in the hills of the western Galilee still shows the signs of the severe soil erosion that transpired in previous centuries. At present the soil profile is thin and basement rock is often exposed. Historical and Biblical sources suggest that the hills in the past were more forested. Therefore, the delta 15N values of dissolved nitrate were measured in radiocarbondated groundwater to see if evidence for past soil conditions could be deduced. Nitrate mineralization processes in soils lead to enrichment in 15 N of the residual nitrate, which being dissolved by rain enters into the groundwater without further isotopic fractionation. Previous studies have shown that there is a trend of increasing delta 15 N in a soil profile from plant, to litter, to the organic material in the soil. In addition, there is a tendency for higher delta 15 N values to be observed in those samples that have been taken at greater depth in a soil profile due to progressive mineralization and subsequent nitrification of soil organic material. As long as the dissolved oxygen is not depleted, denitrification will not occur to alter the isotopic composition of the dissolved nitrate. The nitrate concentrations and delta 15 N values, water chemistry, tritium and radiocarbon activities were measured from the phreatic outcrop recharge region, and onwards into the confined portions of the Judea Group aquifer and its continuation into the juxtaposed Kurdani and Pleistocene aquifers. The radiocarbon activity decreases with flow. Tritium values of above 2 TU are restricted to the recharge region. Using an initial 14 C activity of 64 pMC the radiocarbon ages of the water are found to range from recent to 7800 BP. The delta 15 N values of the dissolved nitrate within the young water recharge area fall in the range of +3.1 to +4.8› (Air), having a mean of +3.9› (n=5). In older water the nitrate concentration increases slightly, while the delta 15 N ranges from +4.7 to +7.2› (Air), having a mean of +6.4› (n=17). The increase in the delta 15 N values in the older water down-dip is not due to denitrification processes; for, the waters are well oxygenated. These older waters infiltrated at the same point of origin in the phreatic portions of the aquifer (non-contaminated) as the recent water. As the earlier infiltrating water flowed down dip they retained the delta 15 N values of the environment at that time. The delta 15 N values present evidence that, compared to the present, the soil and plant cover was better developed in earlier times, including Biblical times.